Quantum jump from singularity to outside of black hole

Abstract

Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be nonunitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitarity in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.

A Model of Black Hole Evaporation and 4D Weyl Anomaly

“…24 There are many interesting approaches for the information problem. In [37][38][39], analyses are made based on an infalling observer, and in [40][41][42], the black hole is identified with a gravitational Bohr's hydrogen atom.…”

“…Using these boundary conditions and the conservation laws (38) and (39) with the assumption (32), we obtain (see Appendix A for the derivation):…”

Black Hole Entropy from Entropy of Hawking Radiation

“…• At the end, we mention that the analysis presented here has been motivated by studying number of photons vs. the entropy of Hawking radiation elaborated in Ref. [28].…”